I received this e-mail from Aaron McMahon. He asked a question that comes often to me from readers living near diverse public schools:

“I live in Alexandria and my child will be starting high school in the next couple of years. I really like living in Alexandria, but I get constant pressure from family that I should move as they all say T.C. Williams is a bad school. I saw in your ratings the other day that you had T.C. ranked very low at 87.

Jay Mathews is an education columnist and blogger for the Washington Post, his employer for 40 years. View Archive

“In your opinion can a student get a quality college prep education there? Why is T.C. ranked so low? . . . I really don’t want to move from Alexandria, and there is no way I could afford Bishop Ireton.”

I told McMahon that it was my fault that he had a wrong impression of T.C. Williams. Alexandria’s single high school has terrific teachers, involved parents and one of the newest and best-equipped buildings in the area. It sends graduates to the most selective colleges. I should have done more to emphasize that a rank of 87 on my local High School Challenge list, based on participation in college-level exams, is actually a very good sign because, on average, we have the most challenging high schools in the country.

T.C. Williams ranks in the top 4 percent of all public high schools measured by participation in college-level courses and exams. Thirty-one percent of its graduating seniors in 2011 passed at least one AP test, nearly twice the national average.

With McMahon, I used this automotive metaphor: Your 2007 Mercedes may not seem so hot in a McLean neighborhood full of brand-new luxury sedans, but it is still a great car.

It is wrongheaded and unproductive to judge schools by the family backgrounds of the students, but we all do it. T.C. Williams has a different reputation than most schools with its academic strengths because 55 percent of its students are from families poor enough to qualify for federal lunch subsidies and 69 percent are black or Hispanic.

Whenever I interview people around the country about their local schools, they tend to praise those where most of the students are affluent and criticize those where most are poor. Having a large number of black or Hispanic students will also hurt a school’s reputation, but in most cases, such schools also have a majority of children whose parents never went to college and don’t make much money. It is class, not race, that makes the big difference.

Children from low-income families have a disadvantage. On average, they don’t get the same opportunities to learn in their early years that affluent children do. It is difficult to catch up when you start far behind. That reduces the average test scores of the schools they attend. Because T.C. Williams has mostly low-income kids, it has lower scores on state tests and has been labeled low-performing.

But its great record on the more challenging AP tests shows that high standards and great teaching can produce a splendid academic environment even if the state test scores are low. Garfield High School in East Los Angeles once had two hard-working teachers whose students included 26 percent of all Mexican Americans in the country who passed the AP Calculus exam, a mind-blowing achievement. But because 85 percent of Garfield’s students were low-income and its average state test scores were far below average, people in Los Angeles considered it a bad school.

I once wrote a 4,000-word piece about misconceptions of T.C. Williams and similar schools for the Washington Post Magazine. T.C. Williams graduate Ben Webne, who went to the University of Virginia, told me that he treasured the friendships he was able to develop in high school with people different from him.

The piece is hard to find on the Internet, so I sent McMahon a copy. If you want one, e-mail me at the address below, and then tell me what you think.

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Comments our editors find particularly useful or relevant are displayed in Top Comments, as are comments by users with these badges: . Replies to those posts appear here, as well as posts by staff writers.